To determine the correctness of the given statements, we need to understand the concepts of "flood fringe" and "floodway" as they relate to floodplain management.

Flood Fringe: This is the portion of the floodplain that lies outside the floodway. It is typically the area where development may be allowed with certain restrictions or provisions, like elevating structures above the base flood elevation. It is not solely reserved for the passage of floodwaters.

Floodway: This is the central part of a river's floodplain, where floodwaters are primarily located during a major flood. The floodway is maintained to carry floodwaters and prevent blockages, so strict regulations typically restrict development in this area to minimize the risk of damage and prevent increased flooding elsewhere.

Based on these definitions, let's evaluate the statements:

1. Statement I claims that the flood fringe is reserved for flood flow passage with no development. This description actually fits the floodway, not the flood fringe. Therefore, Statement I is false.
2. Statement II claims the floodway allows development subject to regulations. In reality, the floodway generally restricts development to ensure it remains clear for effective floodwater passage. So, Statement II is false.

Since both statements misrepresent the definitions and typical management practices regarding flood fringe and floodway, the correct answer is:

Both Statement I and Statement II are false.

Thus, the conclusion reinforces that understanding the precise definitions and uses of floodplain areas is crucial for correctly interpreting exam statements. To correctly answer such questions, one should be well-versed with specific environmental management terminologies and their applications.